Question

How do you solve for $w$ in $S = Lw + wh + Lh$?

Answer 1

Hint: In this question we will use grouping to take out common terms and rearrange the equation such that the term $w$ is on one side of the equation and the rest of the terms are on the other side of the equation.

Complete step-by-step answer:
We have the given expression as:
$S = Lw + wh + Lh$
Since the term $w$ is common in the first and the second terms, we can take it out as common and write the expression as:
$ \Rightarrow S = w(L + h) + Lh$
Now on transferring the term $Lh$, from the right-hand side to the left-hand side, we get:
$ \Rightarrow S - Lh = w(L + h)$
Now on transferring the term $(L + h)$ from the right-hand side to the left-hand side, we get:

$ \Rightarrow w = \dfrac{{S - Lh}}{{L + h}}$, which is the required solution through which we can solve for $w$.

Note:
It is to be noted that the terms $S,L,h$ and $w$ are quantities or terms, which we do not know about, on change in the value of any one or more terms, the value of $w$ will change accordingly.
It is to be remembered that when a term is transferred across the $ = $ its sign changes, which means if the number was positive it becomes negative and if it was negative it becomes positive.
Same happens with terms which are in multiplication and division when transferred across the $ = $ sign.
It is to be noted that the sum of the terms $L$ and $h$ should not be $0$, if the sum of $L$ and $h$ adds up to be zero, then in the denominator of the fraction, we will have $0$, which is a fallacy because a number cannot be divided by zero.